The biochemical case against new genes evolving
The primary focus of this article is genes that code for new proteins, although many of the issues also relate to other types of gene, e.g. those coding for RNA. There are 4 stages to the case why it is prohibitively improbable (realistically impossible) for such genes to arise in an evolutionary way.
1. Most proteins have a very specific (and hence highly improbable) amino acid sequence.
Proteins are linear sequences of amino acids. Typical short proteins are about 100 amino acids long (most are much longer), there are 20 different types of amino acid, any of which can theoretically be at any position in the sequence; so the number of possible sequences is truly astronomical (in fact much bigger than that!).
But, for almost all proteins, in order to function the sequence must be very specific (some variation in sequence is permissible, but for most proteins this is strictly limited).
What this means is that the number of sequences that might work is an infinitesimally tiny fraction of the theoretically possible number of sequences; i.e. realistically there is no hope of coming across a sequence that works by chance. And of course the same is true of the nucleotide sequence (in DNA) coding for the protein.
2. Proteins could not have started off as short sequences.
The prima facie improbability of protein sequences has been known for a long time, and is accepted by most proponents of evolution. However, this improbability in itself is not enough of an objection, because of course proponents of evolution argue that proteins would not have arisen in one hugely improbable step, but would have evolved progressively, e.g. from shorter (even if less effective) sequences (for which of course there are fewer sequence possibilities, which would improve the odds of coming across a sequence that works). This is what evolutionary textbooks say (if they say anything about how new genes might have arisen), but a little investigation shows that there are substantial objections to this.
The two main reasons against proteins starting off as short sequences are:
2.1 Proteins need to fold, and this requires a minimum length of about 70 amino acids
Although proteins are linear sequences of amino acids, in order to have biological function they need to fold up into a 3-dimensional shape.
To be able to do this it needs to be possible to pack the amino acids very closely together - rather like a 3D jigsaw (whilst still being connected together in a linear sequence). The forces between the amino acids (holding them together) are very weak and to have enough overall force to hold the protein in its folded state requires the protein to have a minimum of about 70 amino acids.
This fact is generally completely ignored in speculative scenarios of how proteins might have evolved, with some textbooks even suggesting that proteins could have started off with just a handful of amino acids. But that simply would not work.
2.2 Key amino acids are dispersed throughout the length of the amino acid sequence.
In most proteins, key amino acids such as those that contribute to an enzyme’s ‘active site’, are generally scattered throughout the linear amino acid sequence, and are brought together only once the protein has folded. For example, three amino acids involved in the active site of the digestive enzyme chymotrypisn are a histidine at position 57 in the sequence, aspartic acid at position 102, and serine at position 195.
If proteins had evolved from short sequences, one would have expected that at least these critical amino acids (which must have been close together in a short protein) would still be grouped together. Because to disperse them during the course of subsequent evolution would require restructuring the protein, which would incur the same sort of improbability that the postulated short proteins are intended to overcome. (And bear in mind that the restructuring would need to have been effected in small steps, each with a reasonable chance of happening and offering some advantage that could be favoured by natural selection.)
3. Any evolution of a protein-coding sequence must be in association with other sequences that identify it as a gene
The protein-coding sequence is only part of a gene. By itself, a stretch of DNA that (potentially) codes for a protein, will not result in the production of that protein. At the very least, for a stretch of DNA to be recognised as coding for a protein, at its ‘upstream’ end there has to be a particular (regulatory) sequence to identify the following sequence as coding for a protein. (It will signal the protein-coding sequence to be transcribed into mRNA which will then be used to direct production of the protein.)
That is, even if a sequence that codes for a viable protein should arise, unless it has an upstream regulatory sequence, the organism has no way of ‘knowing’ the coding sequence is (potentially) useful, so it is likely to degrade by mutation, and be lost. Similarly, a regulatory sequence by itself has no utility unless it is followed by a protein-coding (or similarly useful) sequence, and is also likely to be lost.
Hence, because natural selection has no foresight (it cannot ‘see’ potential usefulness), both the regulatory sequence and the protein-coding sequence must be viable: one without the other will not do. This means that for even the most rudimentary of proteins requires an extraordinary coincidence of both sequences (protein-coding and regulatory), arising independently, and yet being viable, and in the right order along the DNA, and probably not too far apart.
The above considerations:
that short proteins will not fold,
that key amino acids are dispersed throughout a protein’s amino acid sequence, and
that a (potentially) protein-coding sequence is useless without being associated appropriately with other sequences that ensure it is recognised and used,
are plain to any with a reasonable knowledge of biochemistry. Yet they are almost never mentioned in evolutionary accounts of how proteins might have evolved. Is this just a blind spot (blinded by the presumed ‘truth’ of evolution), wishful thinking, or deliberately evading inconvenient facts?
Yet that is not all …
4. Most proteins are dependent on others for their activity, which exponentially increases the odds against proteins evolving
The problems against the evolution of any individual protein are compounded because most proteins do not act alone but are dependent on others.
So, for example, consider where two proteins are required for a particular function (and neither protein has any use by itself): If one were somehow to arise, because natural selection has no foresight, it cannot know its potential usefulness (when the second protein is also available); so the first protein will not be kept in reserve for the future, but will be degraded by mutation, and lost. In other words, if a function requires two proteins then both must arise more-or-less together. Which, given the improbabilities against a single protein arising (see above), would require an incredible coincidence of extraordinary coincidences.
Most biological functions require many mutually dependent proteins, not just two; and the improbability of evolving these increases exponentially with each additional protein required. It is this compounding of improbabilities that completely defies an evolutionary origin for new genes.
 For example, for a protein 100 amino acids long, the number of possible sequences is 20100 (20 multiplied by itself 100 times) which is about 10130 (1 with 130 zeros) which is much larger than the number of atoms in the universe (estimated at about 1080).
 Called van der Waals forces, see https://en.wikipedia.org/wiki/Van_der_Waals_force.
 Jack Kyte, Structure in Protein Chemistry, Garland Publishing (1995) p243.
 For example, see Monroe Strickberger, Evolution, Jones and Bartlett (1996), p61.
 Wiki chymotrypsin https://en.wikipedia.org/wiki/Chymotrypsin
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